Crystal Bases for Quantum Affine Algebras and Combinatorics of Young Walls |
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Authors: | Kang Seok-Jin |
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Institution: | School of Mathematics, Korea Institute for Advanced Study 20743 Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-012, Korea. sjkang{at}kias.re.kr |
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Abstract: | In this paper we give a realization of crystal bases for quantumaffine algebras using some new combinatorial objects which wecall the Young walls. The Young walls consist of colored blockswith various shapes that are built on a given ground-state walland can be viewed as generalizations of Young diagrams. Therules for building Young walls and the action of Kashiwara operatorsare given explicitly in terms of combinatorics of Young walls.The crystal graph of a basic representation is characterizedas the set of all reduced proper Young walls. The characterof a basic representation can be computed easily by countingthe number of colored blocks that have been added to the ground-statewall. 2000 Mathematical Subject Classification: 17B37, 17B65,81R50, 82B23. |
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Keywords: | quantum affine algebra crystal basis Young wall |
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